A "change of basis" is an action performed in linear algebra, whereby a change in fundamental structure yields an entirely new viewpoint. This blog began as a record of a pedagogical change of basis for me, and continues as an ongoing account of my thoughts as I design and direct courses in mathematics at the University of North Carolina, Asheville.

Wednesday, September 06, 2006

Class went pretty well today, I thought. (As always, I'd be interested in hearing the student take on this assessment...) The team quizzes were great, the individual quizzes were better, and there was some serious row-reduction of matrices goin' on in our hands-on approach to chemistry. Due to the size of some of the matrices which arose from those chemical reactions (6-by-7 in some cases!), I don't think many people managed to get their reactions to balance through linear algebraic methods. (One notable exception was Deidre: while at first her coefficients didn't come out right, she soon caught her small error in arithmetic a few row operations back, and hey presto! the balanced reaction popped out. Props, Deidre, if you're reading this!)

Anyhow, things went well, and I'm happy to say that it looks like folks are really getting the hang of using matrices to solve linear systems.

A couple of folks have mentioned that it's hard to focus one's attention on the highlights of a day's reading without knowing exactly what those highlights are. To try to address this weakness in the course design, I've begun (with today's class) to provide a short "focus" session at the beginning of class, in which we spend about five minutes hitting the major points of interest from the reading for that day's class. Jeremiah recommended this particular idea to me this morning, and I think it worked out really well today. (Props, Jeremiah!) I'll try to make that a regular part of the class, and students should feel free to comment on how it went today, and how we can make it work better in the future.

On deck for Friday: matrix inverses. I plan on bringing in some geometric applications that might be of especial use to any of the folks whose projects involve geometry (Crystal Gazers and Screen Flickerers take note).